Modeling God’s Attributes and the Biblical God is a Scientifically … · 2015. 12. 30. ·...
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Modeling God’s Attributes and the
Biblical God is a Scientifically Rational Concept.
Robert A. Herrmann, Ph.D.*
21 Aug. 2005. Last revision 30 DEC 2015.
Abstract: In this article, the intuitive aspects used to model mathemat-
ically God’s Biblically implied attributes are presented. These include
the Omni-concepts, miracles and Holy Spirit inspired mental influ-
ences. Although defined mathematical symbolism is employed, the
findings are fully described essentially in non-technical terms. These
results counter all secular statements that claim that aspects of the
Biblically described God concept are “irrational.” The results specif-
ically show that they are rational from the viewpoint of (classical)
everyday logical discourse.
1. Introduction.
In 1978 (Herrmann 1979, 93), a method to model God’s Biblically described at-
tributes (characteristics) and ability-to-act as they are compared with human attributes
and ability-to-act was devised. The modeling technique is based upon Genesis 1:26,
which allows for such a comparison. God has attributes that are not so comparable.
As discussed below, collections of such attributes and ability-to-act may also be used to
model other theological concepts. The most basic results, as mathematically obtained,
were first presented to the scientific community in 1981(a), then to the mathematics
community (1981(b)). After this, they were presented to the general public (1981c).
(I point out that the mathematical reasoning used follows the same logical patterns as
the common everyday logical patterns that human beings must continually use to func-
tion within our physical world. In general, this is modern Mathematical Philosophy -
mathematically modeling of what have been considered as pure philosophic notions.)
In 1979, using the 1978 methods, the foundations for the General Grand Unifica-
tion (GGU) Model and the General Intelligent Design (GID) Model were developed.
The mathematical portion of these models is rather complex and is not presented in
this article. However, their significance is discussed. Are these mathematical models
valuable?
Consider why it is necessary that God, as Biblically described, be a “rational”
notion.
[T]here is no way of explaining the thousands and thousands of contradic-
tions, perplexities, difficulties, and inconsistencies in which religion belief
involves us . . . (Feuerbach, 1967, p. 110).
* Professor of Mathematics (Ret.), The United States Naval Academy, Annapolis,
MD, U. S. A. Vixra:1312.0203 E-mail [email protected]
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[A]theism is a complete and thoroughgoing rationalism (Feuerbach, 1967,
p. 248).
Christianity, . . . , cannot agree with reason because “worldly” and
“religious” reason contradict each other (Marx, 1960, p. 24)
[M]etaphysics is an anti-dialectic method in thought (Marx and Engles,
1960, p. 351).
[T]he grand contradiction is the idea that the same God who is the ideal of
human aspiration is also the creator of the Universe and the only primary
substance (Santayana, 1905, p. 159).
All humanists agree that religion is not based on reason (Eysenck, 1973).
It is a fact that, for hundreds of years, atheistic philosophers and scientists have
claimed that a supernatural God, as Biblically described, is an “irrational” notion.
Indeed, this belief is particularly paramount today. But, if the basic attributes of the
Biblical God can be modeled mathematically, then, since such a model uses scientific
logic (i.e. portions of common (i.e. classical) logic), this atheistic mind-set is falsified.
Moreover, if it can be shown that each physical-system and alterations in the behavior
of such systems follow God’s creationary attributes, then this also falsifies a Santayana
type statement and would give a vast amount of indirect evidence for the existence
of the Biblically described God. Obviously, the existence of such models should be a
valuable theological contribution.
However, some claim that the world of the spiritual and faith should not be ap-
proach via logic and reasoning and that establishing Biblical rationality contradicts the
notion of “faith” - an assumption of what is being expected or a conviction concerning
matters which are not being observed. This is utterly false. There is no human action
that in any manner interacts with the physical world in a direct way that does not
require, at the least, classical logic.
Hundreds and hundreds of times a day each human must apply the simplest aspect
of such logic since observable physical behavior requires it. A healthy human brain
is “wired up” in a manner that requires it. One cannot write or read a statement
without using simple logical procedures. Just opening a door requires it. Indeed, it is
required anywhere an experientially learned cause-and-effect process is applied. Such
an application is equivalent to a statement like “If I push on this type of door, it should
open. So I push on it.” The mathematical reasoning that produced the General Grand
Unification Model uses such classical logic.
The modeled logical process that leads to the attribute-model is a higher-
intelligence form of this “trivial” cause-and-effect logic coupled with a linguistic ab-
breviation that is trivially applied and often not formally stated. For any appropriate
expressions A, B and C, the abbreviation corresponds to “If A and B and C are fact,
then A is fact. If A and B and C are fact, then B is fact. If A and B and C are fact ,
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then A is fact.” The everyday logical processes employed yield no contradiction to the
theological notion of faith.
The Bibles states that one should neither add to nor subtract from
it. This does not merely include words and phrases but concepts as well.
All of my creationary science and theological writings adhere to the follow:
No one should accept that, throughout Biblical times, God deceives His
followers. That is He lies to them. However, beginning after the death of
Apostle John, this is exactly what is proposed by philosophers. They use
forbidden methods of discourse (Col 2:8).
The claim is that His ideas and concepts as originally presented within
the Bibles pages are faulty. That is, they claim that the strict (common) or
obvious nuances in meanings for Biblical terms used therein are incorrect
and have other meanings that have been hidden until revealed after the
death of Apostle John. This claim must be rejected. These other meanings
even contradict strict or obvious nuances. God notes when He sends a de-
ception. Any such alterations in the common meanings or obvious nuances
for the words as understood during Biblical times would make the entire
Bible untrustworthy and even contradictory and, hence, useless except for
possible historical information.
For the New Testament, faith (pistis) is the noun form of the verb “(to) believe”
(pisteuo) and, since the time of Sophocles, is strongly related “to obey” (peitharcheo).
This comes from peitharchos (obeying a superior or authority). A measure of ones
belief in an authority is an individual’s obedience to the rules and regulations put forth
by the authority. So, one needs, at least, to strongly and continually attempt to follow
the behavioral rules put forth by Jesus and other appropriate Old Testament rules from
God as well as those presented by Jesus’ Apostles, including Paul. One needs to use
continually the ordinary patterns of logical thinking in order to obey.
Faith is the acceptance of an hypothesis in a scientific sense, “a conviction concern-
ing matters which are not being observed.” Hence, such an hypothesis is only indirectly
verifiable. That is, when events occur, then this indirectly verifies our previous convic-
tion relative to the occurrences of the events. Today, we can observe a specific molecule
but not its constituents. We do not directly observe a neutron or God in His entirety.
When one accepts a statement by faith, then it needs to produce logical consequences.
If this is not done, then as James states it, faith without “works” (i.e. acts) is “dead,
being alone” (James 2:17). These logical conclusions lead to indirect evidence that the
“faith” hypothesis is fact.
The only question is which type of logical argument yields predicted indirect ev-
idence. Marx and Engles held that only their dialectic form of logical argument is
correct when discussing philosophic concepts. Such a belief is false.(**) Philosophic
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concepts once deemed as not scientific can now be discussed via scientific logic. Estab-
lishing the scientific rationality of God’s attributes leads directly to God’s rationally
obtained behavior. It also refutes those medical professionals who state that anyone
who “hears” from God is behaving irrationally and is mentally ill.
In this article, the attribute-model is specifically described. However, it is signifi-
cant that all known cosmological models, whether secular or theological, are generated
by the GGU-model processes. This means they all follow the rules for common logic.
God’s foreknowledge (future), knowledge of the past and present, all aspects of human
behavior and that of our universe are rationally modeled. (Generally, the term “model”
usually means that it is constructed via the common (scientific) logic and this is how
it is used in the remainder of this article.) The GGU-model also models the notion of
human choice. As mentioned below other theological notions are also modeled.
Relative to the remaining portions of this article and church doctrine,
1 Cor. 15:1-2 implies that a church’s doctrine should have no adverse affect
upon salvation if an individual follows the teachings of Jesus and the Apos-
tles as originally presented. In the original New Testament manuscripts,
the meanings of the terms are as understood during the first-century AD.
These meanings need to be maintained and should not be altered. Clearly,
any contradictory doctrine must be avoided.
2. Main Article
Many, many years ago a list of all of the claimed Biblical (common logic) contra-
dictions was analyzed. After some effort, it was shown that none is as claimed. But, is
a strict Genesis 1 interpretation for creation rational? There is a model [A] that shows
that the Genesis 1 scenario is a scientifically rational account.
In this present article, it is shown that God’s Biblically stated attributes that
have a special form are, in our present material world, strength restrictions of “higher-
attributes.” Ps 147.5 and Isa 55:8-9 state that, at least, two of God’s attributes, His
understanding and His thoughts, are greater than those of any biological entity within
our universe. The modeling process states that members of a collection of higher-
attributes, when displayed in our physical world, are comprehensible by humankind
as specific human-like attributes. The strength of each displayable and comparable
attribute is still greater than a comparable human attribute. There are attributes that
are not comparable to any human attribute.
After rational models are established for various Biblical concepts, then can we use
generalization, as done in inductive science, and state that God’s knowable behavior
is rational? As in physical science, this is the “faith” part. For example, God is
a Spirit. Is the Spirit notion a rational notion? Yes, since there is a mathematical
model for various characteristics of His Spirit. The Spirit of God is, at least, partially
characterized by properties that we can comprehend. Can we know every aspect of
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how His Spirit behaves? No. Do we need to accept various things based on faith? Yes.
Are there common logical contradictions in the Bible? No. So, the entire Bible can be
added as part of a rational model for God’s behavior.
What does it mean to state that Jesus is the Son of God? This statement occurs
over forty times in the New Testament. In the Greek language, the term “son” need
not correspond to a biological son or an adopted son. If an individual A has “nearly”
the same characteristics as an individual B, then B can refer to A as his “son” and A
can refer to B as his “father.” Apparently, this is how “Son” should be interpreted in
these many cases, but in the strongest possible sense.
In physical science, two entities differ if their defining characteristics differ. This
difference can be in but one characteristic or parameter. Further, not all characteristics
need to be listed or even known in order to differentiate an entity from all others. This
is an important principle.
In all of these modeling procedures, meaningful words and phrases
are representations for physical or physical-like events or meaningful
concepts. How the words are rationally combined represents physical or
physical-like behavior or meaningful conceptual relations.
Using Herrmann (1979, 93, pp. 23-24), consider B as a list of God’s Biblical
attributes written in a form that can be qualified by the word “very.” (It should
be self-evident that other words such as “great” or “greater” or “stronger” can also
be used.) These words can carry a meaning that includes God’s ability-to-act upon
something and produce results. Most members of B are similar to comparable human
attributes and include the ability-to-act in specific cases.
Each member of B can be specially expressed in a required word-form.
For example, in this list are words such as “intelligent, understanding, cre-
ative, just, loving, knowledgeable, powerful, etc.” These are to be qualified
by use of the word “very.” Then words like “mercy” “ability-to-act” are
to be qualified by a term such as “greater.” In place of “mercy,” the term
“merciful” can be employed and this term is quantified by the term “very.”
This also applies to “wrath” and others. The phrase “great ability-to-act”
appears stronger than just the word “ability-to-act.” The Biblical concept
of a Saviour is included in B by simply using this term in B. It is qualified
by the repeated use of the term “great.” The term “saviour” has meanings
other than that of an ultimate Saviour. It will be such an ultimate Saviour
when the modeling is complete.
Additional aspects of God’s Spirit are partially characterized in B by
expressing His “omni” properties. For omnipotent, use “powerful” as the
basic word and for omniscient use “knowledgeable.” Each point (location)
within our physical universe is contained in an entity called a “monadic
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cluster.” Except for the physical point, no member of the monadic cluster
is observable. They are members of the “substratum” (Herrmann, 2002, p.
170), a preternatural world. Most likely, it is through the monadic clusters
that God’s Spirit affects the physical world.
For omnipresent, start anywhere within our universe and consider a
cubical configuration of space. This yields a specific collection of monadic
clusters, one for each point, that contains (or covers) this configuration.
The physical cube has an edge 1 foot long in terms of a fixed measuring
stick. Call this collection a “cubical-MC-space.” Each cubical-MC-space
has a vast set of entities that are not members of physical space. Let the
word “cubical-MC-space” be a member of B. From the standpoint of spatial
size, it makes sense to use the qualifier “larger (and)” for this word, where
“larger” means to add a foot in length to the cube’s edges.
The monadic clusters represent a medium through which God’s Spirit
acts and such actions can occur instantly throughout the entire universe by
application of hyperfast subparticles (Herrmann, 2002, p. 163). The model
predicts that, at least with respect to the physical world since the monadic
clusters are omnipresent, that God’s Spirit is omnipresent. In this model,
the “omni-concepts” are, most likely, enough to differentiate God’s Spirit
from all other Biblically mentioned entities.
The mathematics also yields a rational model for a highly significant
New Testament concept. It presents a rational description as to how the
Holy Spirit influences our “minds.”
When the foundations for a mathematical model are specified, they are often
straightforward. But, from such a simple basis, a highly complex mathematical theory
can emerge. Such a theory can then be used to “model” other discipline notions via
terminology changes. What follows is an example of this process.
The basic intuitive idea is that an attribute being described by such a phrase as
“very intelligent” is “stronger than” or “better than” or “greater than” or a similar
phrase than the attribute described by the word “intelligent.” The attribute being de-
scribed by the phrase “great ability-to-act” is “greater than” simply having an “ability-
to-act.” Further, we would have that “intelligent” is “weaker than” the attribute “very
intelligent.” One continues with this intuitive notion and considers the attribute being
described by the phrase “very, very intelligent” as stronger than the attribute described
by the phrase “very intelligent.” One uses the informal idea of “mathematical induc-
tion” and obtains a set BP that contains each member of B and all of the strings of
arbitrary finite length that qualify members of B, the “very, very, . . . , very b,” “great,
great, . . ., great b,” etc. strings of symbols, where b denotes a basic member of B.
The entire construction of this model yields the (Grundlegend-Deductive) GD-world or
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GD-world model.
A special form of simple logic is also identified. Due to the forms involved and not
due to the rules of grammar, this special form of logic is called “adjective reasoning.”
Intuitively, this form of reasoning takes any member c of BP and logically yields the
member c of BP and all of the other members that may be “weaker than” c. For
example, let b = “very, very intelligent.” Taking b and applying the specified rules for
this logical process yields {“very, very intelligent,” “very intelligent,” “intelligent” }.
Adjective reasoning can also be viewed as a very simple restriction of one of the most
basic forms of human thought - propositional deduction. Propositional deduction is
a basic part of the classical (common) logic used throughout scientific and everyday
discourse.
Now comes the somewhat more difficult part. All of these intuitive notions are
turned into standard mathematical objects by a coding process and they are embedded
into the mathematical theory that includes the basic theory of natural or rational or
real numbers, as necessary. I note that this is just what happens in modern digital
communication and what is done to communicate with a computer. For a computer,
each of these word-forms is considered as coded by a binary representation for a natural
number - a string of 1s and 0s like 1001 = 9. The coding for the attribute-model is not
of this binary type. In what follows, the coded results are denoted by bold face type.
Thus, BP denotes the coded and embedded set BP. Then BP is further embedded into
a rather complex mathematical object called the Grundlegend structure (Herrmann,
1979, 93).
A mathematical theory, in form, is most simply understood as a collection of
symbols, where technically each symbol has no non-mathematical meaning. When
one, in a consistent manner, substitutes for various mathematical symbols meaningful
words or phrases from another discipline or a different portion of mathematics itself, an
interpretation is produced. The entire substitution process yields a mathematical
model.
Scientifically such interpretations yield the must highly consistent, rational and
predictive collection of statements obtainable by a human mind using portions of clas-
sical logic. This is exactly what is done in the case of BP when it is viewed from the
Grundlegend structure. The theory automatically generates the mathematical object
*BP. The set *BP is predicted. It is not part of the hypotheses used. Significantly,
there are additional mathematical objects in *BP that are not in BP.
Yet, a more difficult part is investigating the properties of those members of *BP
that are not in BP. The major result for this application is Theorem 4.4.1 (Herrmann,
1979, 93, p. 46). This is what has been discovered. Take any member b of B. Then there
is an object d in *BP, which is not in BP, with the following “interpreted” properties.
One cannot actually write down the complete form the object d takes, although it has
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conceptional meaning. We can write down portions of it and mentally be aware of its
construction. What we know, in general, is that it mathematically exists and some of
its properties. For example, d’s behavior with respect to the “better than” ordering
can be expressed. The only question would be which type of logical argument yields
the consequences?
Consider any finite string of symbols “very, very, . . . b” in BP. Then d is
“better than” “very, very, . . . b.” When adjective reasoning A is coded and viewed
mathematically, a “higher form” of adjective reasoning *A is predicted that contains
the original idea of adjective reasoning.
Using ∗A applied to d, each “very, very, . . . b,” no matter how many
“very”s are placed next to the b, is obtained. What this means is that
if d is interpreted as a Divine higher-attribute, then the collection of all
the weaker attributes are also used, in a comparative means, to partially
describe the Divine higher-attribute.
“God is good. God is very good. God is very, very good. God is very, very,
very good. etc. ” (Great care must be taken here when considering the word “good.”
Indeed, the model explicitly shows that such a collection of modified attributes is a
logical consequence associated with a “higher-intelligence.” This is not to be taken in
some general sense. It refers to a specific compatible attribute.)
Adjective reasoning *A, as viewed from the Grundlegend structure, reveals a higher
form of reasoning that, when restricted to members of BP, models human adjective
reasoning. This verifies one aspect of Genesis 1: 27. God has given us some of His
reasoning power. Since b is arbitrary, then these characteristics hold for any member
of B. Note that in all cases of which I am aware, this human form of reasoning is equiv-
alent to a portion of “scientific” reasoning. Further, these results have been rationally
established by means of scientific deduction.
What this intuitively implies is that each Divine higher-attribute being
modeled is “infinitely stronger than” or “infinitely greater than” the cor-
responding attribute of any biological entity. Such results do not restrict
God’s attributes nor their strength. This includes the Spirit attributes. It is
enough to characterize that Spirit as an entity that is infinitely knowledge-
able, infinitely large, and infinitely powerful. These three statements are
usually enough to differentiate His Spirit from others. The same approach
yields the Saviour aspect of God’s attributes.
Using the mathematical theory ZFC that establishes these results,
there is no ultimate bound in ZFC for the concept of “infinitely stronger
than.” For a somewhat more technical explanation, see the article [B]. Ra-
tionally, these results do imply that such ultimate bounds can be assumed
to exist. This verifies the additional faith requirement.
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[Note: The processes A and *A will yield extraneous results (i.e. forms). However,
using the recently discovered notion of the general logic-system (Herrmann, 2001, 2006,
2006a), the A and, necessarily, the *A can be restricted so as to remove all of the
extraneous results.]
Within physical science, and especially quantum physics and early his-
tory cosmology, the actual objects discussed cannot be directly observed.
These objects are defined by their measurable and describable character-
istics. Their existence is “indirectly” surmised by their observable predic-
tions. Thus, using this acceptable indirect approach, aspects of human
behavior and human reasoning yield indirect evidence that there rationally
exist objects characterized by those members of ∗BP, the higher-attributes,
that are not contained in BP. (Symbolically this set of higher-attributes is
denoted by ∗BP− BP.)
I repeat a few of the remarks made in the article [C]. The Scriptures state that
“Christ is the image of (’the invisible’ in the Sinaiticus Codex) God,” 2 Cor. 4:4, and
“He is the image of the invisible God,” Col. 3:10. For these two Biblical statements and
due to the Greek for “invisible,” Vine states, that Jesus is “essentially and absolutely
the perfect expression and representation of the Archetype (pattern), God the Father,”
and that “Christ is the visible representation and manifestation of God to created
beings” [Vol. II, p. 247]. Here, relative to invisible, this means to “see” with the eyes.
This and the first-century common meaning of the term “logos” and “allos” in John
14:16 imply the term “Jesus” (or the “He” (it, him, he) as the Greek auto (the same) is
translated) has a much broader meaning than the observable physical representation,
the Christ.
As noted, there is also the use of the word “another” as it is used in various
translations, where the most ancient Greek manuscripts use two different words. In the
KJV and NIV, the Greek word “allos” is translated as “another” in John 14:16, and
a different word “heteros” is translated as “another” in Romans 7:23. But these have
two considerably different meanings.
In order to have a nonempty set Λ of entities each must have, at least, one common
feature. Then two members A and B of Λ can share many or even most of their
additional attributes. For a common understanding of the Greek “allos,” usually Λ
has more than two members, and the selected A and B share many or most additional
attributes. Of course, being different entities it is often stated that they share “similar”
attributes. In John 14:16, the general category is that what is to be presented is a
“comforter.” But “allos” is employed. In Johns 14:18, Jesus tells His apostles the
common features of this new comforter. He states, “I will come to you.”
The term “heteros” signifies entities in Λ but with many different attributes when
compared. The term “different,” or similar terms depending upon the category, should
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be used rather than the word “another.” The Jerusalem Bible, Today’s English Version
and New English Bible use “different’,” while, as mentioned, the KJV, NIV use the
term “another.” So what Paul states in Romans 7:23 is that it is a type of “law” but
of a considerably different sort.
Let a set of describable and pre-ascension (physical universe) restricted Father
attributes and ability-to-act (i.e. the ability to perform necessary actions) be denoted
by FA. This set contains all of knowable attributes comparable to human beings. It
does not include the restricted omnipresent attribute.
The set FA is a mathematically model that is interpreted. That is, FA is con-
sidered as a model, a representation, for a set of knowable, restricted and Biblically
stated Father attributes and implications based upon them. The set FA itself need not
contain all such knowable attributes. The actual set FA is a subset of BP. This same
representation concept is used throughout this article.
Let the strength restricted Son of God attributes contained in BP be denoted RS.
Let HS denote restricted Holy Spirit attributes. (Note: Various effects of Holy Ghost
attributes that are members of HS are displayable. The attributes are mental in that
the Holy Ghost refers to aspects of the Spirit of God interacting, after Jesus is perfected
and in a special way, with our minds. For example, it “guides and comforts us” and
has other personal characteristics.)
The man “Jesus” has human characteristics that are not Father attributes. Jesus
always displays human attributes as well as Divine actions. This is not a contradiction
since Divine actions employ a non-physical immaterial medium. When Jesus “speaks”
or behaves in various ways, one needs to determine whether He is displaying His phys-
ical and non-Father human characteristics or actions, or His Father characteristics or
actions or, indeed, under certain circumstances, both simultaneously. In all cases, the
action of “speaking” is a human action. When He speaks or acts as a man, vari-
ous Divine attributes are not displayed. At other times Jesus speaks as God would
speak or performs actions that display His Divine attributes. This is all relative to
the circumstances under which His attributes are displayed. His human attributes are
displayed most often during His earthly existence. As pointed out by Colin Brown, this
is consistent with both Phil 2.7 and Isa 53 (Brown, 1975).
Notice that, in John 14: 15-20, Jesus states explicitly that the Holy Ghost will
display His attributes. Further, Jesus also displays a restricted form of the “creation”
attribute. An important step is taken when it is realized, using John 10:30 and the
John 14:9-11 notion of ”image,” that, at least, in the physical-world
RS = FA (1).
This indicates that, as a man, Jesus’ attributes are maximal. That is, a phys-
ical entity can have no more powerful nor greater Divine attributes than those that
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indwelled Jesus in either of His forms. There is a difference between having certain
attributes and displaying these attributes. Not all of the FA attributes were displayed
during Jesus’ physical life-time. He displayed physical attributes while in His glorified
form that He did not display previously.
But, is there more that can be done using this mathematical approach? Consider
the Biblical notion of “being perfect” or “being complete” or “mature.” The Scriptures
state in Matthew 5:48 that one of the Father attributes is being perfect. Also in Hebrews
2:10, 5:9, we find that the supernatural Jesus is perfected. Consequently, being complete
is an attribute of the Father and, in general, an attribute of God.
The Biblical notion of “complete” can be modeled by adjoining to the set BP
additional word-forms that include the simplest logical implication associated with
“completeness.” This yields the coded set of comprehensible word-forms BPC. For this
investigation, a set is “complete” if it can be logically demonstrated that it contains all
objects that satisfy a specific requirement. A special logical process P, strong reasoning
from the perfect, is defined (Herrmann, 1979, 93, p. 38). (This P is obtained by using
a restricted form of propositional deduction.)
In this model, the set *BPC is used as a representation for the hyper-
comprehensible God. (A comprehensible attribute is also hyper-comprehensible. hyper-
comprehensible is a comparative notion. In order to “understand” what all members
of *BPC - BPC signify, a higher language and higher “thought” processes must be
applied.) The set BPC contains the three sets that model the restricted completed
Father, FAC, the restricted completed Son, RSC and the restricted completed Holy
Ghost, HSC, attributes. Since RSC is strength restriction, it does not immediately
follow that FAC = BPC. Depending upon how completeness C is constructed, appli-
cation of Theorem 4.3.5 (Herrmann, 1979, 93, p. 43) and strong reasoning from the
perfect logical operator P yields a rational derivation for equations
∗P( ∗FAC) = ∗P( ∗RSC) = ∗P( ∗HSC) = ∗BPC (2).
[The construction of the C part of the word-forms that yields (2) can easily be seen
to yield BPC when P is applied to FAC and HSC. The model predicts the “hyper
property.” It is not unusual to construct models in this manner since the significant
part is that this is an analogue model designed to produce rationally obtained behav-
ior. That is, expression (2) is rationally obtained. One can argued or accepted that
the special construction is the one God intended when the notion of completeness is
assigned to members of FA and HS. This construction appears necessary if His Spirit
is considered as inseparable. For those that might reject the Vine description, (1) can
be modified and we only need that RS is a nonempty subset of FA. That is, only one
attribute in RS is necessary if it also carries the perfection requirement.]
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The equations in (2) can be difficult to interpret when one considers that ∗P
represents a higher-intelligence. However, they do have a significance interpretation
when viewed from the Biblical “Third-Heaven.”
Using the operator ∗P to obtain the Third-Heaven view, the super-
natural entity being described by ∗P( ∗RSC) cannot be differentiated from
the other two within this Third-Heaven. All three represent a perfect en-
tity, which is represented by perfect ∗BPC. The set ∗P( ∗RSC) is also a
representation for the glorified Jesus.
Equation (2) has been established via mathematically (scientific) reasoning and
is not dependent upon expression (1).(*) Although, equation (2) can be discussed and
interpreted informally, humankind cannot actually mimic the logical process ∗P. A
strong indication that we cannot as yet properly comprehend the total meaning of∗P( ∗RSC) is that its equality with ∗P( ∗FAC) implies that the modeled Spirit “omni”
properties also hold for ∗P( ∗RSC).
Additionally, equation (2) satisfies, at the least, four different notions. Which
of these notions one accepts requires additional sources of rational information if one
wishes to make an intelligent and rational Biblical choice. The notion of “choice” is
one way to determine intelligent actions. The actual attributes that produce (2) are
the three sets of C extended attributive collections FAC, RSC, HSC.
It is important to realize prior to interpreting (2) that this is a model
and as such it does not “prove” that (2) or an interpretation is fact. It shows
that the interpretations are classically rational. This counters the atheistic
statements quoted above. Evidence for an interpretation can come from
many sources, the first being a strict interpretation of Biblical statements.
In this case, recall the original meaning for the word that denotes a complete log-
ical expression of a thought. The complete logical and personal expression of Himself
the complete Jesus mental-like concept - the logos - exists and does not cease to exist,
from our comprehension, before, during and after the thoughts are manifested. The
notion that it comprises “thoughts” and the consequences of the thoughts goes back to
Heraclitus at about 500 B. C., where the consequences of these thoughts yield material
entities. But, for its Biblical usage, such thoughts also produce the non-physical. In
general, God’s thoughts exist, in a sequence sense, prior to being manifested as physi-
cal, preternatural or supernatural entities. Entities are comprehended by listing their
attributes whether they are displayed or not. This holds for the Jesus manifestations as
they relate to God. Equation (2) yields rational information about these manifestations
via interpretations.
In the following, the ordering of the A - D statements does not indicate a pre-
ferred ordering. Intelligent choice, as based upon additional information,
is advocated.
12
Consider the classical notion of “truth” and “falsity” relative to basic conditional
statements. Let a statement “If A, then B” be true, where A and B are any other
meaningful statements. This signifies that when “A” true, “B” is true. But, when “A”
is false, the original statement does not tell one whether “B” is true or false. In fact,
the conditional “If A, then B” is false in only one case, when “A” is true and “B” is
false. Now consider the statement “A if and only if B” or many similar ones. This
statement is true in only one case, when both “A” and “B” are true. Some church
organizations falsely claim that for a specific “A” and “B” the Bible teaches that “A if
and only B,” when in reality it only teaches “If A, then B.”
For what follows, there is a vast amount of literature relative to (B). This is the
reason that the discussion for (A) is more extensive than for (B).
(A) It is rational to state that the three related attributive descriptions, FA,
RS, HS, signify that the Spirit of God manifests itself within the physical world in
specific Biblically described ways and these manifestations can be grouped, at least,
into three categories as observed within the physical world. These manifestations of
God’s attributes are a major aspect of His “planned” creation activities. The best
way to comprehend this is to use “mind” terminology. Each collection is a mental
description, where God transforms His thoughts into various realities. This is the tri-
category model. First and foremost, the restricted FA = RS. Although not necessary,
one can state that each of these collections displays aspects of God’s personal relation to
humankind. Indeed, each set can be classified as exhibiting certain characteristics that
can be described as “personality-traits.” Such manifestations are grouped in this way
for better comprehension and they are not disjoint. “Personality-traits” are knowable
behavioral traits that are the same as or similar to human behavior, or that interact
with humans in such a way as to influence behavior.
The one Spirit of God is inseparable and God uses an immaterial medium to
actuate each restricted manifestation. One can conclude, using this tri-category model,
that part of the complete expression of this Divine concept is that, if necessary, God will
present Himself to His created physical universe via RS. In this case, RS is a special
strength restriction and displayable manifestation of the Jesus attributes described in
completed form by ∗P( ∗FAC) = ∗BPC.
Note that, in this model, when Jesus is “perfected” in the sense of ∗BPC, then the
glorified Jesus displays attributes that were not displayed prior to His perfection. This
follows since these attributes are not displayable by Jesus the man using His restricted
attributes. Further, as the supernatural Father, God can refer to Himself in various
ways, such as emphasizing the completed ∗RSC without it contradicting this rational
model. Significantly, taken in this complete form, the personal relationship between
God and each member of His church is emphasized.
God has many different viewpoints. This rationally obtained model specifically
13
shows that, from one major viewpoint, a display of any nonempty collection of His
attributes amounts to the display of all of them. That is, in this case, He does not
actually separate His attributes in any manner. It is humankind that makes such a sep-
aration. This separation is not part of God’s character for the Third Heaven viewpoint.
As mentioned, if this behavior is carried over to His spirit, then this also means that
His spirit cannot be separated. These properties are accepted by various Christians.
As usual, not all predictions made by a model need to be accepted. Hence, in simple
terms, we have the following description.
(****)Jesus, as He appears during His earthly ministry, is a type of
special restriction of all of God’s attributes that can be associated with
a physical human being and displayed within a physical universe. He is
the absolute representation of the Father to the created universe and more.
The attributes displayed depend upon the circumstances. He also displays
during His earthly ministry purely human attributes as well. Potentially, via
God’s spirit that indwells Him, Jesus, the man, represents all of the Father
attributes that are displayable in the Third Heaven environment. As the
glorified Jesus, He displays attributes that He did not display while in an
ordinary human form. More generally, the following statement expresses
this (A) Jesus concept.
Jesus is the personal name of the Father when His behavior relates to
His created entities. Further, the Father exhibits this behavior when His
attributes are restricted to circumstances, whether physical or otherwise,
that can or do influence human beings in any of their physical or non-
physical forms. When any such behavior is perceived by any of His created,
then such behavior carries this additional identification. The first Biblical
instance of this behavior is His creationary activities in Genesis 1. The last
Biblical occurrence of such activity is stated in Revelations 22.
God’s comparable attributes will always remain infinitely greater than any of those
of His created, no matter what form His created may take. Further, He has attributes
that we cannot, at present, comprehend. There are other questions that most likely
require the Third Heaven language to answer. One is, “Will His created, in any form
they take, ever know God in any other way except as He is represented by the glorified
Jesus?” Some say no, as based upon the equation ∗P( ∗FAC) = ∗P( ∗RSC). They
state that the glorified Jesus is the only Father entity that His glorified Church will
“ever” encounter.
(B) It is pointed out during the analysis of the Greek term “logos” in [C] and [D]
that the meanings of certain terms such as this one might be altered by later revela-
tions. If you believe that this is possible, then you can accept a more complex notion
described by Justin Martyr and completely revealed after nearly 800 years of “progres-
14
sive revelation.” In this case, one needs to modify his description and accept a distinctly
different concept - the classical Trinity. In this case, all the Biblical statements that
imply expression (1) and the relation between Jesus and the Holy Spirit require altered
meanings.
What was generally stated can now be specified for this case. In general, thoughts
represented by RSC, ∗RSC, HSC and ∗HSC exist. This case assumes that ∗FAC,∗RSC and ∗HSC just don’t represent distinct ideas, but distinct entities. That is, that∗FAC, ∗RSC and ∗HSC describe distinct supernatural objects that share the basic
attributes that would classify them as God and they use the same medium to manifest
themselves in the physical world. Then equation (2) is interpreted as a unification
statement. It represents the shared God attributes. Historically, there have been seven
different methods suggested to unify these three collections. Indeed, some theologians
have stated that how these three are unified can be classified as a “mystery.” The
“perfection,” in this case, refers to the required “God” underlying structure that allows
one to state that the three distinct entities are “God.”
This case is rationally obtained by first separating BP into various appropriate
collections and than applying the entire mathematical process to each of the collections.
Then the non-separable property holds for each of corresponding higher-attributive
collections. In this case, attributes of God have been separated.
(C) Some theologians suggest a third possibility. For them, equation (2) does not
apply at the moment that Jesus is perfected, but rather at a moment near the end of
Revelations. At that moment, their interpretation states that the distinct entities of
(B) are unified in such a manner that they can no longer be differentiated one from the
other.
(D) There is yet another interpretation some use. The equation (2) ∗P( ∗FAC) =∗P( ∗RSC) is an exact equivalence of the supernatural Jesus and the Father and indi-
cates the unification. The ∗HSC equivalence is simply ignored.
The two basic interpretations, (A) and (B), for equation (2), although poorly
stated, were published in Herrmann (1982). Interpretation (A) is rationally obtained
from the rationally predicted equation (2). Interpretations (B), (C) and (D) follow
from hypotheses termed as revelations and they probably do not follow rationally from
Biblical statements. Notice that if one uses sets such as ∗BPC as a model for God’s
Spirit with all of its attributes, then, as noted below, His Spirit is not separable in that
one “piece,” so to speak, cannot be differentiated from His entire Spirit.
Objects such as BPC are composed of specific members that are additionally
characterized as being “finite.” This notion is transferred to ∗BPC and is part of the
“language” that can be employed by members of God’s glorified church. “Expressions”
from this language are hyper-comprehensible and carry an additional mathematical
characteristic. Only such objects are hyper-comprehensible within this Third Heaven
15
(2 Cor. 12:2). In 1 Cor. 13:12, Paul states that we will comprehend more. But, in
many places, such as Job 28: 13, Ps. 139: 6, Isa. 55: 8-9, Rom. 11:33, the statements
imply that, in general, God has incomprehensible behavior partially represented by
members of ∗BPC − BPC.
Within the Third Heaven, it is sufficient that His glorified church view∗P( ∗RSC), ∗P( ∗FAC), ∗P( ∗HSC) as representing identical objects (eq. (2)). This
helps to explain why God identifies, in a specific manner, the ∗P( ∗RSC) collection
(the perfected and risen Son - the Glorified Jesus) as the most significant and hyper-
comprehensible representation since it includes all aspects of His personal relationship
with His physical creation and His church. Since technically RS is contained in ∗RS
which is contained in ∗P( ∗RSC), then ∗P( ∗RSC) also represents God’s abilities
to accomplish tasks - His power - as the Biblical term “dunamis” signifies. (He is
powerful; very powerful; very, very powerful; etc.) It is significant that the collection∗P( ∗RSC) represents all of the hyper-comprehensible knowledge of God’s compara-
tive behavior that any of His created beings, in any of their allowable forms, can ever
“comprehended.”
When a mathematical model is proposed, it is not necessary that each of the
derived conclusions be included within an interpretation. Indeed, in general, only a
few are and the remainder are considered as extraneous. However, there is yet another
interesting result that explains, for many, what may seem to be a rather humanly
incomprehensible property.
The Theorem that yields equations (2) yields another result. Let set A be
any nonempty collection of BP entities. Of course, this includes the case where A
contains only one member. Then adjoin the “perfect” notion C to A. This yields the
set AC. Applying Theorem 4.3.5, we have that
∗P( ∗AC) = ∗BPC (3).
Result (3) is not the same result as (2). This formally establishes the rationality
of another mentioned interpretation. It is that, from the Third Heaven viewpoint,
God’s attributes, in general, are not separable. That is, if God displays just one of
His higher-attributes, then, from this viewpoint, that one higher-attribute represents
all of His higher-attributes. This conclusion is similar to (A). But, equation (3) and
this interpretation can be ignored. On the other hand, the set ∗BPC can be used as
a model for Spirit material, which it predicts as inseparable.
Because (A) - (D) present different possibilities, on needs to make a informed
choice. Is acceptance of (A), (B), (C) or (D) necessary for salvation? If this were the
case, then Moses, Abraham and other members of the original “people of God” would
not be saved from the “fiery pit.” Moreover, the Bible implies, even in the description
of the New Jerusalem in Rev. 21, that the Apostles are saved. And, there is no Biblical
16
indication that they had to choose from a list such as (A) - (D) to achieve salvation.
How significant is extra-biblical doctrine? According to Paul’s statement 1 Cor. 15:2, if
church doctrine does not adversely affect the actual Biblical methods the Apostles teach
and that lead an individual to salvation, then “believing anything else (the additional
church doctrine) will not lead to anything.” (Jerusalem Bible). That is, Paul states
that such church doctrine is not significant.
“Brothers, I want to remind you of the gospel I preached to you, the gospel that
you receive and in which you are firmly established; because the gospel will save you
only if you keep believing exactly what I preached to you - believing anything else will
not lead to anything.” 1 Cor. 15:1-2 (Jerusalem Bible). I cannot found in Paul’s stated
doctrine that such a selection is necessary.
After about 33 AD, salvation does result, via faith in Jesus, by accepting him as
the Lord and Saviour, by believing in Him, trusting Him and obeying Him. Paul’s
doctrine contains the implications established from John’s gospel. What is presented
here may further illuminate the basic meanings of the Biblical terms when they were
first transcribed. If one needs additional reasons to follow the doctrine of Jesus and
the Apostles, then this presentation might be useful.
The mathematics that appears in Herrmann (1979, 93, pp. 27-56) can be used to
model other theological notions that some would consider less significant and, in some
cases, highly speculative in character. Some of these are associated with C. S. Lewis
descriptions. In this short article, I will not consider any other material that appeared
in the original G-model book.
In Aug. 1979, I was challenged to solve the General Grand Unification problem.
The problem is to find a collection of mathematical objects, from a specific category,
that unifies all physical-system behavior. Consider two statements:
“The structure of the material universe has something in common with
the laws that govern the working of the human mind.” Louis De Broglie
“. . . events in the remotest parts of space appear to obey the laws of
rational thought. . . . According to it what is behind the universe is more
like a mind than it is anything else we know.” C. S. Lewis.
My original solution to this problem began with the notion of a scientific theory.
All such theories use human thought processes to predict physical behavior from a set
of hypotheses. Not withstanding the Lewis statement, the solution is not based upon
any desire to model mathematically any Divine attribute. I postulated that a solution
to this problem involves a collection of mathematical objects that model “thought pro-
cesses.” The question then becomes, what thought processes and what mathematical
objects would solve this problem. The actual mathematical structure used is not one
of the usual standard structures, but the solution requires a “nonstandard” structure.
17
General nonstandard structures were not discovered until 1961 and applying nonstan-
dard analysis to thought processes had not been done.
The problem is solved, in the main, by applying standard and nonstandard analysis
to certain operators (Herrmann (1979, 93, pp 65-128) that, at the least, represent the
most basic aspects of human thought. For this application, an “operator” models
processes in a specific manner. When an operator is applied to a set of hypotheses X,
it predicts all of the conclusions that can be rationally deduced from X. In the 1930s,
Tarski introduced operators that accomplish this. They are not well known. These are
the consequence operators (or operations), which I have shown are equivalent to the
general logic-system. General logic-systems yield details that such operators do not.
Logic-systems are used to obtain, via a simple deductive process, ordered collections.
In the simplest case, an operator A, based entirely upon one basic rule of inference,
models the human ability to take a finite collection of objects and “order them” in a
specified manner. In a similar manner, one obtains the “gathering” operator that con-
joins simple objects to form a more complex object. This yields the “info-fields.” One
final operator, “the realism operator,” yields the physical universe. These operators are
used so that we can comprehend how the master operator, which is their composition,
behaves. Basic operators are coded and their properties are investigated using nonstan-
dard analysis. The results are the GGU-model and the GID interpretation. I note that
the term “nonstandard” does not mean there is anything wrong with the mathematics,
it is a technical term. These models are all obtained using modern set-theory.
After the secular GGU-model was constructed, it became obvious that this model
can be interpreted in a manner that models various Divine attributes. Among these
various attributes are His Biblically stated creationary methods, the notion that God
designs all physical-system behavior and entities and yet allows choice, that God is a
higher-intelligence, that God sustains the behavior of all physical-systems within our
universe and that physical-systems display signatures for God’s higher-intelligence. It is
also predicted that when a universe develops “ultranatural” events are produced. Very
little can be known about these events. They can influence the physical world. They
probably correspond, in some unknown way, to the relation between the non-physical
and the physical worlds. They can even yield behavior aspects of the invisible human
“spirit.” Or, they can merely be repeated physical events. Further analysis may yield
a better understanding as to the purpose for the predicted ultranatural events.
3. The Rationally of Additional Major Influences that
Directly Affect Humanity.
Two more operators have been discovered (Herrmann, 2004). When theologically
interpreted, one can be interpreted as yielding sudden alterations in our physical world
that can be classified as miracles events. Moreover, the two verify Biblical statements
that imply that supernatural influences affect human thought processes. Of course, the
18
GGU-model in its pure secular form need never be interpreted theologically.
When I explicitly think and when I read, I do so in words or images. I “hear” a
mental voice. It does not have the same characteristics as the sounds I hear via my
audio senses, sounds that emanate from sources physically external to my brain. It
has a quality that does not change. The qualities it has seem to match my own voice.
The mental images are considerable different from those that I perceive via my visual
sense. I mentally “talk” to myself. I make the assumption that all individuals who do
not exhibit hallucinations have these same experiences.
“One feature of linguistic expression is rarely considered in depth. We
can all recognize that when we are attempting to express subtle thoughts,
particularly those that are novel and as yet unclear, we may tentatively
try now this, now that verbal expression. In fact this is precisely what is
done in writing this section. In attempting to convey some experience it
is difficult to give satisfactory verbal expression to one’s thoughts. One
searches for the right words and syntactic arrangement so that one can
have hope that one’s thoughts may achieve a clear expression to listeners
or readers.” (Eccles and Robinson, (1984, p. 117))
John Eccles is a Nobel Laurent world authority in the electro-chemical behavior
of our brain. He won this prize for identify such electro-chemical activity. Of course,
there are many that attempt to discount his views based only upon a non-scientific
philosophic stance and nothing else.
Although there have been attempts to explain physically how such mental im-
pressions occur, none that I have investigated is satisfactory from a physical-science
viewpoint. This does not invalidate the view that somehow or other, such “thoughts”
are self-generated. On the other hand, there might be causes that are classified as
non-physical and these produce such mental results. In Herrmann (2006), I discuss ap-
plication of the mathematical results in Herrmann (2004) to the Eccles and Robinson
(1984) and Popper notion that there are immaterial aspects of human thought,
aspects that indirectly relate to such mentally obtained results. They claim
that there is no reasonable explanation for how our thoughts behave, un-
der certain specific circumstances, except to assume that they are being
influenced by an immaterial medium.
Evidence indicates that this Eccles and Robinson conclusion should be
somewhat generalized to other mental thought patterns. That is, that a
much larger category of thoughts can be influenced by immaterial exterior
sources.
For almost 2000 years, detailed observations and personal testimonies imply that
“immaterial” processes that influence aspects of human thought and corresponding
behavior may, indeed, exist in objective reality. Today, as based upon scientific disclo-
19
sures, my observations indicate, that it is, at least, probable that some human behavior
is being so influenced. It is rather remarkable that Paul, relative to Christian notions,
should present descriptions as to how mental influences can govern our thoughts.
Paul states a “law” that “evil is present within” (Rom. 7:21) even when he tries
to “do good” and that the “god of this world,” in some manner, tries to control human
behavior. He writes (underlines added) “the god of this world hath blinded the minds
of them which believe not” (2 Cor. 4:4). He also states, “the carnal mind is enmity
against God” (Rom. 8:7). Paul sees that this “law” is warring against the law of his
mind and “bringing me into captivity to the law of sin” (Rom. 7:23). Further, an
individual can be “vainly puffed up by his fleshly mind” (Col. 2:18). As to what is
the “law of his mind,” he states, “So that with the mind, I serve the law of God”
(Rom. 7:25). Paul also states that indwelled Christians have the “mind of Christ” (1
Cor. 2:16). “And he that searcheth the hearts knoweth what is the mind of the Spirit,
because he maketh intercession for the saints according to the will of God” (Rom 8:27).
“And be not conformed to this world: but be ye transformed by the renewing of your
mind” (Rom. 12:2).
In Hebrews, quoting from the Old Testament, we find that for God’s laws “in their
minds I will write them” (Heb. 10:16). Paul makes it very clear what type of influence
he considers paramount, “Let this mind be in you, which was also in Christ Jesus”
(Php. 2:5). Experience and Paul’s observations clearly imply that the war between
“good and evil” is within the mind of each individual. When one has knowledge of what
constitutes these two categories, then mostly mental arguments lead an individual to
choice one behavior over another.
Theorems 2.1 and 2.2 in Herrmann (2004) and the definitions in that paper yield
a model that implies that immaterial entities can influence how human thoughts are
expressed. Individuals apply physical processes based upon a collection of “standard
rules.” The standard rules state that a physical process applies under specific cir-
cumstances. These standard rules contain various parameters that must be specified
or other requirements that must be met prior to physical-process application. When
these standard rules are embedded into the mathematical structure used for the GGU-
model, another set of rules is predicted to exist, the “ultranatural-rules” (UN-rules)
that include all of the standard rules.
Various members of the set of predicted UN-rules that do not correspond to a
standard rule differ from the original rules in that they cannot be completely decoded
and, hence, cannot be completely presented using humanly comprehensible sensory
information. Most of these UN-rules cannot even be partially presented. For this
reason, it can be rationally assumed that there are, at the least, actual UN-rules that
govern application of the processes here discussed as they are modeled by “mixed logic-
systems.”
20
Under the basic assumption that what is mentally heard is produced by physical
brain functions, then, for each individual, what is mentally heard is based upon the
semantic knowledge stored. For this application of Theorems 2.1 and 2.2, it’s assumed
that the words and images, as mentally expressed, have meaning for an individual. All
such words, sentences, paragraphs, etc. as well as images are represented by objects in
a language L. Indeed, as mentioned, members of L can model all human sensory
information.
When L is encoded and embedded into a special mathematical structure, an addi-
tional representative nonstandard language ∗L is mathematically predicted to exist.
The actual members of the embedded L form a set L of abstract mathematical objects.
These objects are interpreted as the embedded members of L and each member of L
can be decoded to obtain its corresponding member in L. This is not the case with
members in ∗L that are not members of L (Notation: members in ∗L − L.) Under
extensive analysis, portions of these objects might be decoded, but not an entire object
in ∗L−L. There is a vast array of members from ∗L−L that cannot even be partial
decoded. We do know, however, that the set ∗L behaves in many ways exactly like a
representative informative language. The set of all UN-rules is a subset of ∗L, that is
each member of UN-rule is a member of ∗L.
Relations between members of L can represent the black-box generated physical
processes that yield the mental words one hears or images mentally perceived. You
insert a statement like “How can I do that?” Then the mental voice states “Move the
chair next to the small table and put the telephone book on it.” I need not consider
how this answer is physically obtained, only that it is the result. This creates a process
relation just like those that occur for known physical laws.
From the mathematical model point of view, the v = “How can I do that?” and
the w = “Move the chair next to the small table and put the telephone book on it”
are single objects called (mathematical) “words.” All such processes, where a mental
statement or image leads directly to a related expression or image, can be expressed in
this manner. Of course, w and v are assumed to be some sort of actual physical entities
within the brain that are perceived in this manner.
The empirical material processes and entities being modeled are as follows: (1) The
enthymeme notion. (2) How humans try to strength their spoken or written influences
by repetition.
(1) In almost all informal arguments, all of the hypotheses being used
are not stated. They are supposed to be understood by the audience to
which the statements are addressed. The enthymeme notion is just that,
deduction based upon unstated hypotheses. But, to the uniformed, they
are hidden and, often due to this, a logical argument may be difficult to fol-
low. The “hidden hypotheses,” and more generally hidden statements, are
21
missing. These hidden statements contain meaningful information relative
to other nearby statements.
(2) To emphasize what has been written or more likely stated, we often
repeat over and over again the same idea, but maybe in different terms. This
is a major method within political science.
For (1), using the mathematical theory, the following interpretation is predicted.
For a certain w, an immaterial source determines its mental occurrence. For this
to occur for this model and for a particular v, an addition “immaterial object” is
inserted into the black-box. Such an object is predicted to exist. This immaterial
object is the “hidden” statement. Such a hidden statement is represented in whole or
in part by members of ∗L − L. For this article, I denote some members of ∗L − L
by α, β, γ, δ, ǫ, . . . , χ, . . ., etc. These are used to “represent” various “immaterial
mental influences” that, along with a v, yield a specific mentally perceived w.
Thus, if you mentally have a v, then to obtain a particular w one of the immaterial
entities uses an “interface” type of process requiring, at the least, one χ input. This
produces physical brain reactions. The physical products, the w type expressions, of
this process are determined by nonstandard elements such as γ. The actual modeling
process shows that the mental “appearance” of such a w is caused, in part, by the
presence of such a γ, where the γ is required in order for the v to yield w. This process
is modeled by an ultra-logic-system and corresponds to a specific ultralogic. It is called
an influencing process.
[The ultra-logic-systems presented in Herrmann (2004) are informally presented.
They can easily be predicted by formally considering ternary or binary relations for
nonempty finite relations of either type.]
Of course, distinct from the w, there may be other z, which correspond to the
v, from which one can select that are self-generated and no χ is used. Although no
χ has semantic meaning for us, it does have meaning for an immaterial intelligence.
Consequently, in the immaterial case, the w is not self-generated. Generally, mankind
cannot have direct knowledge that the influencing process is being applied, although
under certain circumstances, there are individuals that do have physical manifestations
that such an influencing process has occurred. Of course, there are other w that
one might perceive and that are generated by other influencing processes initiated
by other immaterial sources. It is rather significant that Theorem 2.2 in Herrmann
(2004) shows that the influencing process can occur without there being a v type of
“triggering” statement. This is where influenced statements seem to simply “pop” into
your thoughts.
Theorems 2.1 and 2.2 (Herrmann, 2004) establish that certain collections of objects
that include various χ are equivalent to a corresponding pure ultralogic operator, one
of the operators used within the GGU-model. Such influencing processes resemble
22
logically predicted mathematical operators that are interpreted in a physical-like sense
as is done in quantum physics via the mathematical operator notion. That is, the
addition of various χ yields mathematical objects that behave like processes - the
influencing processes - where the influences are rationally attributed to one or more of
the defined immaterial sources.
For (2), it is shown in Herrmann (2004), how other ultra-logic-systems model the
emphasis process and the strength of such processes can be measured.
Notice that it is rational to assume that there are UN-rules that determine when
and to whom such influencing processes are applied. Assuming that every individual
has the potential to be so mentally influenced, those that are influenced would need
to satisfy certain UN-rule requirements. Although, in general, most members of the
UN-rules cannot be expressed in complete detail, observation can lead to experientially
deduced restrictions of these rules to our physical world. That is, a standard collection
of “rules” that describe and predict human behavior.
The mechanism used to influence our thoughts is via the predicted, not hypothe-
sized, nonstandard language and the application of either of the predicted ultra-logic-
systems and the predicted pure ultralogic operators discussed in Theorem 2.1 and 2.2
in Herrmann (2004). The model is very general in character and further research may
yield other useful predictions. The immaterial existence of these influencing processes is
an indirectly verified hypothesis that yields rational predictions. These mathematically
predicted processes that influence our thoughts and there acceptance as fact are not
just fantastic ramblings for there is a vast amount of evidence that indirectly verifies
that procedures like these rationally obtained influencing processes exist.
Application of the “inverse” of Theorem 2.2 in Herrmann (2004) and the participa-
tor mechanism discussed in Herrmann (2013a) yield miracle events. These are further
discussed in [E].
Thus, the rational existence of the Biblically described God is further
strengthened by considering the Biblical creationary, mental influencing
and miracle producing aspects of God as they are modeled by a theological
interpretation of the GGU-model and the GID-model (Herrmann, 2002).
(*) One of the basic hypothesis used by philosophers is that we can comprehend
the essence, the basic underlying structure, of “something,” by describing it in words.
That “words” used refer to a god.
(**) The arguments used often do not follow common logic but rather follow the
notion of the dialectic argument. It has been shown that, from the viewpoint of common
logic, including the “time” axiom within your rules for a dialectic requires such a time
notion to be non-finite in character.
23
References
Brown, C. “The New International Dictionary of New Testament Theology Vol 1”,
(1975), p. 548-549.
Eccles, J. and D. A. Robinson, “The Wonder of Being Human, Our Brain and Our
Mind,” The Free Press, New York, 1984.
Eysenck, H. J. in “The Humanist Alternative; Some definitions of Humanism,”
(ed) Kurtz, Paul, Prometheus Books, Buffalo, New York.
Feuerbach, L. 1967. “Lectures on the Essence of Religion,” Tr. R. Manheim,
Harper & Row, New York.
Herrmann, R. A. 2013. Genesis 1:1 - 2:1, God’s Mental Behavior and A Genesis
6: 14-16 Noah’s Ark Illustration, http://vixra.org/abs/1312.0122
Herrmann, R. A. 2013a. Nonstandard Ultra-logic-system Applied to the GGU-
model, http://vixra.org/abs/1305.0125
Herrmann, R. A. 2008. Modeling the dialectic, http://arxiv.org/abs/0810.0768
Herrmann, R. A. 2006. General logic-systems and finite consequence operators,
Logica Universalis, 1:201-208.
Herrmann, R. A. 2006a. General logic-systems that determine signifi-
cant collections of consequence operators, http://vixra.org/pdf/1309.0013v1.pdf or
http://arxiv.org/abs/math/0603573
Herrmann, R. A., 2006b. The rationality of hypothesized immaterial mental pro-
cesses, C. R. S. Quarterly, 43:127-129
Herrmann, R. A. 2004. Nonstandard consequence operators generated by mixed
logic-systems, http://arxiv.org/abs/math/0412562
Herrmann, R. A. 2002. “Science Declares Our Universe IS Intelligently Designed,”
Xulon Press, Fairfax, VA.
Herrmann, R. A. 2001. Hyperfinite and standard unifications for physical theories,
Internat. J. of Math. and Math. Sci., 28(2):93-102.
Herrmann, R. A. 1981(a). Mathematical Philosophy 1981 Status Report 1 Annual
Meeting of the American Scientific Affiliation, Eastern College, St. Davids, PA, 23
August 1981.
Herrmann, R. A. 1981(b). Mathematical Philosophy, Abstract of Paper Presented
AMS Notices 2(6)(Oct. 1981):527
Herrmann, R. A. 1981(c). Navy prof. says his formulas prove. . . , The Birming-
ham News, Oct 30, 1981, p. 1B.
Herrmann, R. A. 1982. The reasonableness of metaphysical evidence, J. of the
American Scientific Affiliation, 34(1):17-23.
24
Herrmann, R. A. 1979, 93. “The G-model Applied to C. S. Lewis. The
Mathematics.” This portion of this book is now contained in pages 1 - 64
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able at the Mathematics and Physics Archives. http://arxiv.org/abs/math/9903081
http://arxiv.org/abs/math/9903082
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of the C. C., C. P. S. U., Foreign Languages Publishing House, Moscow.
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Website Files.
[A] A Strict Genesis 1-8 Interpretation.
http://vixra.org/abs/1512.032
[B] Measuring the Strength of God’s Attributes.
http://www.raherrmann.com/measureintell.htm
[C] Who is Jesus? http://www.raherrmann.com/jesus.htm
[D] Who is Jesus - Additional Details. http://www.raherrmann.com/jesus1.htm
[E] A Miracle Producing Mechanism. http://www.raherrmann.com/mirmech.htm
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